j is the midpoint of $ \overline { f h } $ and $ \overline { g i } $. complete the proof that $ \triangle f i j \cong \triangle h g j $.

1 j is the midpoint of $ \overline { f h } $ given
2 j is the midpoint of $ \overline { g i } $ given
3 $ \overline { g h } \cong \overline { f i } $ given
4 $ \overline { f j } \cong \overline { h j } $ definition of midpoint
5 $ \overline { g j } \cong \overline { i j } $ definition of midpoint
6 $ \triangle f i j \cong \triangle h g j $ cpctc definition of congruence sas sss

Question

j is the midpoint of $ \overline { f h } $ and $ \overline { g i } $. complete the proof that $ \triangle f i j \cong \triangle h g j $.

1 j is the midpoint of $ \overline { f h } $ given
2 j is the midpoint of $ \overline { g i } $ given
3 $ \overline { g h } \cong \overline { f i } $ given
4 $ \overline { f j } \cong \overline { h j } $ definition of midpoint
5 $ \overline { g j } \cong \overline { i j } $ definition of midpoint
6 $ \triangle f i j \cong \triangle h g j $ cpctc definition of congruence sas sss

Accepted Answer

# Explanation:
## Step1: Identify the congruent sides
From statements 4 ($\overline{FJ}\cong\overline{HJ}$) and 5 ($\overline{GJ}\cong\overline{IJ}$), and given $\overline{GH}\cong\overline{FI}$ (statement 3).
## Step2: Use the SAS (Side - Angle - Side) congruence criterion
In $	riangle FIJ$ and $	riangle HGJ$, we have two pairs of congruent sides ($\overline{FJ}\cong\overline{HJ}$ and $\overline{GJ}\cong\overline{IJ}$) and the included angles (the vertical angles at $J$ are congruent). By the SAS (Side - Angle - Side) congruence criterion,  $	riangle FIJ\cong	riangle HGJ$.

# Answer:
SAS

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QUESTION IMAGE

Question

Explanation:

Step1: Identify the congruent sides

Step2: Use the SAS (Side - Angle - Side) congruence criterion

Answer: